A conical dry screw vacuum pump rotor structure and design method thereof

Abstract

The present invention discloses a conical dry-type screw vacuum pump rotor structure and a design method thereof, wherein the rotor structure includes a first rotor and a second rotor meshing with each other, and the rotor profile is composed of a point-meshing cycloid segment AB, a tooth tip arc segment BC, a pseudo-polynomial curve segment CD, an envelope curve segment DE of the curve segment CD, and a tooth root arc segment EA. The rotor profile is provided with different tooth width angles and transition line structures at different rotor axial positions, and the angular variation of the rotor profile along the central axis at different axial positions is obtained by defining points A, B, C, and D defined by cubic spline differences. By defining the rotor's cone angle, rotor center distance, initial tooth tip radius, pseudo-polynomial degree and profile width angle in the profile transition line at different axial positions, and cubic spline curve difference points in the rotor variable pitch law curve, the variable pitch variable profile conical screw vacuum pump rotor structure can be flexibly adjusted to achieve flexible adjustment of the working chamber volume variation law.

Description

Technical Field

[0001] The present invention belongs to the technical field of dry screw vacuum pumps, and in particular relates to a conical dry screw vacuum pump rotor structure and a design method thereof. Background Art

[0002] Dry screw vacuum pumps have the characteristics of reliable operation, low cost, no vulnerable parts such as air valves, compatibility with liquids and high operating efficiency. Therefore, they are widely used as equipment for medium and high vacuum environments and in the pharmaceutical, chemical and semiconductor industries. The core components of dry screw vacuum pumps are a pair of mutually meshing rotors, which complete the periodic transportation of gas through the meshing movement of the rotors. In order to realize the volume change process of the working chamber between the rotors during transportation, the rotor structure needs to be set to a variable pitch or conical structure to complete the internal compression transportation process of the gas, reduce energy consumption and exhaust temperature, and enhance the operational reliability of the dry screw vacuum pump. During the gas transportation process, leakage is the main factor affecting its thermal performance. Since the gas pressure in the working chamber between the rotors spans from 1Pa to 10 5 Pa, while there is no oil seal in the cavity. Reducing leakage requires optimizing the rotor structure to adjust the position distribution, geometry, and flow conditions of the leakage channel formed by the gap, thereby effectively controlling the internal gas leakage process. However, the existing conical rotor structure of screw vacuum pumps has a single variable parameter, leaving little room for rotor structure optimization, making it impossible to effectively control the leakage process. This, in turn, limits the performance improvement of existing conical rotors in screw vacuum pumps. Summary of the Invention

[0003] The purpose of the present invention is to address the problems in the above-mentioned prior art and provide a conical dry screw vacuum pump rotor structure and a design method thereof, so as to achieve high design flexibility of the screw vacuum pump rotor structure and thereby improve rotor performance.

[0004] In order to achieve the above object, the present invention has the following technical solutions:

[0005] A conical dry screw vacuum pump rotor structure includes a first rotor and a second rotor meshing with each other. The first and second rotors have the same profile structure. The rotor profile consists of a point-meshing cycloid segment AB, a tooth addendum arc segment BC, a pseudo-polynomial curve segment CD, an envelope curve segment DE of the curve segment CD, and a tooth root arc segment EA. The rotor profile has different tooth width angles and transition line structures at different rotor axial positions. The angular variation of the rotor profile along the central axis at different axial positions is obtained by points A, B, C, and D defined by cubic spline interpolation.

[0006] As a preferred solution, the cone angle of the first rotor and the second rotor is α, and the tooth tip radius of the profile corresponding to the axial position of the rotor is solved as follows:

[0007]

[0008] Where, For the corner The top radius of the rotor profile is For the corner The corresponding rotor axial position and angle Indicates the rotation angle of the rotor profile along the rotor center axis;

[0009] The corner is The corresponding rotor axial position Calculated by the following formula:

[0010]

[0011] Where P(θ) represents the pitch corresponding to the rotor angle θ.

[0012] As a preferred solution, the rotor profiles at different rotor axial positions have the same center distance. The rotor center distance calculation expression is as follows:

[0013]

[0014] Where A is the rotor center distance, For the corner The root radius of the rotor profile at .

[0015] As a preferred solution, the position vector of the point-meshing cycloid segment AB is solved as follows:

[0016]

[0017] Where r AB represents the position vector of the meshing cycloid segment AB, θ represents the parameter variable, R p is the pitch circle radius, equal to A / 2, matrix M i is the unit rotation matrix, which conforms to the following expression:

[0018]

[0019] As a preferred solution, the position vector of the tooth top arc segment BC is:

[0020]

[0021] Where, Indicates the designed tooth width angle of the profile under different rotation angles.

[0022] As a preferred solution, the position vector of the pseudo-polynomial curve segment CD is:

[0023]

[0024] Where, The degree of the pseudo-polynomial design for the profile at different corners;

[0025] The enveloping curve segment DE of the curve segment CD is determined by the meshing relationship with the curve segment CD.

[0026] As a preferred solution, the position vector of the tooth root arc segment EA is:

[0027]

[0028] As a preferred solution, the rotor angle Corresponding pitch Determined by the positions of points A, B, C, and D and the slope at point D, where the slope at point C is 0 and the pitch and corner The relationship is determined by cubic spline interpolation, and the curve segment ABC is expressed as:

[0029]

[0030] Where a 0,ABC ~a 3,ABC are the polynomial coefficients, which can be obtained by the following formula:

[0031]

[0032] Where, P A , P B , P C Respectively represent the pitch defined by points A, B, and C, The corners defined by points A, B, and C respectively;

[0033] The pseudo-polynomial curve segment CD is expressed as:

[0034]

[0035] Where a 0,CD ~a 3,CD are the polynomial coefficients, which can be obtained by the following formula:

[0036]

[0037] Where k D represents the slope at the defined point D.

[0038] A method for designing a conical dry screw vacuum pump rotor structure includes:

[0039] The rotor center distance A, initial tooth tip radius R2(0), and the position of the difference point A and point B on the pitch curve are determined by the exhaust volume requirement;

[0040] Based on the power requirement, define the rotor cone angle α and the position of the difference point C and point D of the pitch curve and the slope k of point D. D , solve the rotation angle as follows: The top radius of the rotor profile is The rotation angle is calculated as follows: The corresponding rotor axial position P(θ) represents the pitch corresponding to the rotor angle θ;

[0041] The following formula is used to calculate the profile tooth root radius corresponding to different rotor axial positions:

[0042]

[0043] According to the determined parameters, the point meshing cycloid segment AB, the tooth top arc segment BC, the pseudo-polynomial curve segment CD, the envelope curve segment DE of the curve segment CD and the tooth root arc segment EA of the rotor profile corresponding to different rotor axial positions are determined.

[0044] As a preferred solution, by designing the rotor cone angle α, the rotor center distance A, the initial tooth top radius R2(0), the positions of the difference points A, B, C and D in the rotor variable pitch regular curve and the slope k of point D D , the design pseudo polynomial degree of the profile under different corners Designed tooth width angle of profile line at different turning angles Adjust the rotor structure of the variable-pitch variable-profile conical screw vacuum pump to adjust the volume change law of the working chamber, optimize the position distribution, geometric structure and flow conditions of the working chamber leakage channel during gas transportation, and obtain the optimal rotor geometry to meet different needs.

[0045] Compared with the prior art, the present invention has at least the following beneficial effects:

[0046] By rationally defining the rotor's cone angle, rotor center distance, initial tooth tip radius, the degree of the pseudo-polynomial in the profile transition line at different axial positions and the profile tooth width angle, and the difference points of the cubic spline curve in the rotor's variable pitch law curve, the rotor structure of a variable pitch, variable profile conical screw vacuum pump can be flexibly adjusted to achieve flexible adjustment of the working chamber volume variation law, optimize the position distribution, geometry, and flow conditions of the working chamber leakage channel during gas transportation, and thus obtain the optimal rotor geometry to meet different requirements. Compared with existing rotor structures, the rotor structure of the present invention can be flexibly adjusted, thereby increasing the performance optimization space based on the existing profile structure, thereby achieving the optimal rotor geometry control to meet different requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 Schematic diagram of the rotor structure of a conical dry screw vacuum pump according to an embodiment of the present invention;

[0048] Figure 2 A schematic diagram of the rotor profile structure according to an embodiment of the present invention;

[0049] Figure 3 Schematic diagram of rotor profiles under different parameters of an embodiment of the present invention:

[0050] (a) Rotor profile structures with pseudo-polynomial orders n of 1.1, 1.6, and 2.1, respectively;

[0051] (b) Rotor profile structures with tooth width angles γ of 60°, 100°, and 140° respectively;

[0052] (c) Rotor profile structures with tooth tip radius R2 of 80 mm, 90 mm, and 100 mm respectively;

[0053] Figure 4 Schematic diagram of pitch variation law in an embodiment of the present invention;

[0054] Figure 5 Schematic diagram of the rotor structure under different design parameters of the embodiment of the present invention:

[0055] (a) Volume variation diagram of the rotor with a cone angle α of 3° under a certain pitch variation law;

[0056] (b) Volume variation diagram of the rotor with a cone angle α of 3° under the regulation of pitch variation;

[0057] (c) Volume variation diagram when the rotor cone angle α is 1° and the pitch is adjusted; DETAILED DESCRIPTION

[0058] The present invention will be described in further detail below with reference to the accompanying drawings.

[0059] The embodiment of the present invention sets the screw vacuum pump rotor structure as follows Figure 1 The cone angle shown is a conical structure, and rotor profiles with different tooth width angles and transition line structures are set at different axial positions. The profile structure and variable parameters are as follows: Figures 2 to 3 As shown in Figures (a), (b), and (c), at the same time, Figure 4 As shown in FIG, the variation law of the rotation angle along the central axis of the rotor profile at different axial positions is obtained by points A, B, C, and D defined by the cubic spline difference.

[0060] The variable pitch variable profile conical screw vacuum pump rotor structure can be flexibly adjusted by reasonably adjusting the design parameters, thereby achieving the following Figure 5 Flexible adjustment of the working chamber volume change pattern shown in Figures (a) to (c) ultimately regulates the position distribution, geometric structure and flow conditions of the working chamber leakage channel during gas transportation, thereby achieving a significant improvement in the rotor thermal performance parameters.

[0061] exist Figure 1 In the conical rotor structure, the cone angle is α, and the rotor axial position and the corresponding tooth tip radius of the profile are:

[0062]

[0063] Where, For the corner The top radius of the rotor profile is For the corner The corresponding rotor axial position and angle Indicates the rotation angle of the rotor profile along the rotor center axis.

[0064] The rotor profiles at different rotor axial positions have the same center distance, that is:

[0065]

[0066] Where A is the rotor center distance, For the corner The root radius of the rotor profile at .

[0067] Rotor axial position and rotor angle The relationship can be obtained by the following formula:

[0068]

[0069] Where, Indicates the rotor angle The corresponding pitch.

[0070] like Figure 2As shown, the rotor profile consists of the point meshing cycloid segment AB, the tooth top arc segment BC, the pseudo-polynomial curve segment CD, the envelope curve segment DE of the curve segment CD and the tooth root arc segment EA. The position vector of the point meshing cycloid segment AB is:

[0071]

[0072] Where r AB represents the position vector of the meshing cycloid segment AB, θ represents the parameter variable, R p is the pitch circle radius, equal to A / 2, matrix M i is the unit rotation matrix, expressed as:

[0073]

[0074] exist Figure 2 In the figure, the position vector of the tooth top arc segment BC is:

[0075]

[0076] Where, Indicates the designed tooth width angle of the profile under different rotation angles.

[0077] The position vector of the pseudo-polynomial curve segment CD is:

[0078]

[0079] Where, It represents the degree of the pseudo-polynomial designed for the profile at different corners.

[0080] Curve segment DE is determined by its meshing relationship with curve segment CD.

[0081] The position vector of the tooth root arc segment EA is:

[0082]

[0083] like Figure 3 As shown, the adjustable parameters of the above-mentioned profile are: center distance A, tooth top radius R2, tooth width angle γ and pseudo polynomial degree n. Adjusting the above parameters can realize flexible adjustment of the profile shape.

[0084] exist Figure 4 In the rotor angle Corresponding pitch Determined by the positions of points A, B, C, and D and the slope at point D, where the slope at point C is 0. and corner The relationship is determined by cubic spline interpolation, where the curve segment ABC is expressed as:

[0085]

[0086] Where a 0,ABC ~a 3,ABC are the polynomial coefficients, which can be obtained by the following formula:

[0087]

[0088] Where, P A , P B , P C Respectively represent the pitch defined by points A, B, and C, The corners defined by points A, B, and C respectively.

[0089] The curve segment CD is expressed as:

[0090]

[0091] Where a 0,CD ~a 3,CD are the polynomial coefficients, which can be obtained by the following formula:

[0092]

[0093] Where k D represents the slope at the defined point D.

[0094] like Figure 5 As shown in Figures (a) to (c), by reasonably adjusting the rotor's cone angle, variable pitch law control points and profile setting parameters, the variable pitch variable profile conical screw vacuum pump rotor structure can be flexibly adjusted, thereby achieving flexible adjustment of the working chamber volume change law.

[0095] The embodiment of the present invention adopts a cubic spline difference curve to define the rotor variable pitch law, and adopts a rotor profile with high design flexibility to achieve the adjustment of the tooth width angle and profile structure at different rotor axial positions. At the same time, a conical rotor structure is adopted, combined with the variable pitch law, to achieve effective adjustment of the leakage tooth width, leakage area and leakage operating conditions of the rotor working chamber.

[0096] The method for designing a conical dry screw vacuum pump rotor structure according to an embodiment of the present invention comprises the following steps:

[0097] The rotor center distance A, initial tooth tip radius R2(0), and the position of the difference point A and point B on the pitch curve are determined by the exhaust volume requirement;

[0098] Based on the power requirement, define the rotor cone angle α and the position of the difference point C and point D of the pitch curve and the slope k of point D. D , solve the rotation angle as follows: The top radius of the rotor profile is The rotation angle is calculated as follows: The corresponding rotor axial position P(θ) represents the pitch corresponding to the rotor angle θ;

[0099] The following formula is used to calculate the profile tooth root radius corresponding to different rotor axial positions:

[0100]

[0101] According to the determined parameters, the point meshing cycloid segment AB, the tooth top arc segment BC, the pseudo-polynomial curve segment CD, the envelope curve segment DE of the curve segment CD and the tooth root arc segment EA of the rotor profile corresponding to different rotor axial positions are determined.

[0102] The position vector of the point-meshing cycloid segment AB is obtained by the following formula:

[0103]

[0104] Where r AB represents the position vector of the meshing cycloid segment AB, θ represents the parameter variable, R p The pitch circle radius is equal to A / 2, the matrix M i is the unit rotation matrix, expressed as:

[0105]

[0106] The position vector of the tooth tip arc segment BC is:

[0107]

[0108] Where, Indicates the designed tooth width angle of the profile under different rotation angles.

[0109] The position vector of the pseudo-polynomial curve segment CD is:

[0110]

[0111] Where, It represents the degree of the pseudo-polynomial designed for the profile at different corners.

[0112] Curve segment DE is determined by its meshing relationship with curve segment CD.

[0113] The position vector of the tooth root arc segment EA is:

[0114]

[0115] Based on the requirements of sealing and processing, define the relationship between the pseudo polynomial degree n and the rotor profile angle The relationship between the tooth width angle γ and the rotor profile angle The rotor profile corresponding to different rotor axial positions can be obtained.

[0116] Variable pitch law of rotor Determined by the positions of points A, B, C, and D and the slope at point D, where the slope at point C is 0. and corner The relationship is determined by cubic spline interpolation, where the ABC curve segment is expressed as:

[0117]

[0118] Where a 0,ABC ~a 3,ABC are the polynomial coefficients, which can be obtained by the following formula:

[0119]

[0120] Where, P A , P B , P C Represent the pitch defined by points A, B, and C respectively, The corners defined by points A, B, and C respectively.

[0121] The CD curve segment is expressed as:

[0122]

[0123] Where a 0,CD ~a 3,CD are the polynomial coefficients, which can be obtained by the following formula:

[0124]

[0125] Where k D represents the slope at the defined point D.

[0126] In summary, according to the embodiment of the present invention, by reasonably designing the cone angle α, the center distance A, the initial tip radius R2(0), the positions of the difference points A, B, C and D of the pitch variable pitch regular curve and the slope k of point D D , the relationship between the pseudo polynomial degree in the design profile transition line and the rotor profile angle The relationship between the profile tooth width angle and the rotor profile angle The flexible adjustment of the rotor structure of the variable pitch variable profile conical screw vacuum pump can be achieved, and then the flexible adjustment of the working chamber volume change law can be achieved. The flexibility of the rotor structure design can optimize the position distribution, geometric structure and flow conditions of the working chamber leakage channel during gas transportation, so as to obtain the optimal rotor geometry structure that meets different needs.

[0127] The above-described embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A conical dry screw vacuum pump rotor structure, characterized in that: The invention comprises a first rotor and a second rotor meshing with each other, wherein the first rotor and the second rotor have the same profile structure, and the rotor profile is composed of a point meshing cycloid segment AB, a tooth top arc segment BC, a pseudo-polynomial curve segment CD, an envelope curve segment DE of the curve segment CD, and a tooth root arc segment EA; the rotor profile is provided with different tooth width angles and transition line structures at different rotor axial positions, and the rotation angle variation law of the rotor profile along the central axis at different axial positions is defined by the cubic spline difference. A 、 B 、 C 、 D Points obtained; The cone angles of the first rotor and the second rotor are α , the tooth tip radius of the profile corresponding to the rotor axial position is solved as follows: Where, R 2( φ ) is the turning angle φ The top radius of the rotor profile is L ( φ ) is the turning angle φ The corresponding rotor axial position and angle φ Indicates the rotation angle of the rotor profile along the rotor center axis; Corner φ The corresponding rotor axial position L ( φ ) is obtained from the following formula: Where, Indicates the rotor angle The corresponding pitch; The point meshes with the cycloid segment AB The position vector of is solved as follows: Where r AB Represents a point meshing cycloid segment AB The position vector of θ represents parameter variables, R p is the pitch circle radius, equal to A / 2, matrix M i is the unit rotation matrix, which conforms to the following expression: The pseudo-polynomial curve segment CD The position vector is: Where, n ( φ ) represents the design pseudo-polynomial degree of the profile at different corners; The envelope curve segment DE of curve segment CD is composed of the curve segment CD Determined by the meshing relationship.

2. The conical dry screw vacuum pump rotor structure according to claim 1, characterized in that: The rotor profiles at different rotor axial positions have the same center distance. The calculation expression of the rotor center distance is as follows: Where, A is the rotor center distance, R 1( φ ) is the turning angle φ The root radius of the rotor profile at .

3. The conical dry screw vacuum pump rotor structure according to claim 1, characterized in that: The tooth top arc segment BC The position vector is: Where, γ ( φ ) represents the designed tooth width angle of the profile under different rotation angles.

4. The conical dry screw vacuum pump rotor structure according to claim 3, characterized in that: The tooth root arc segment EA The position vector is: 。 5. The conical dry screw vacuum pump rotor structure according to claim 3, characterized in that: rotor angle φ Corresponding pitch P ( φ ) by the definition point A ,point B ,point C ,point D Position and point D The slope at which the point C The slope is 0, the pitch P ( φ ) and corners φ The relationship is determined by cubic spline interpolation, and the curve segment ABC Expressed as: Where, a 0,ABC ~ a 3,ABC are the polynomial coefficients, which can be obtained by the following formula: Where, P A , P B , P C Represent points A 、 B 、 C The defined pitch, φ A , φ B , φ C Separate points A 、 B 、 C The defined corner; The pseudo-polynomial curve segment CD is expressed as: Where, a 0,CD ~ a 3,CD are the polynomial coefficients, which can be obtained by the following formula: Where, k D Indicates the defined point D The slope at .

6. A method for designing a conical dry screw vacuum pump rotor structure according to claim 5, characterized in that: include: The rotor center distance is determined by the exhaust volume requirement A , initial tooth tip radius R 2(0), pitch curve difference point A with dot B Location; The rotor cone angle is defined by the power requirement α Difference point with pitch curve C with dot D Position and point D The slope k D , solve the rotation angle as follows: φ The top radius of the rotor profile is R 2( φ ): , calculate the rotation angle as follows φ The corresponding rotor axial position L ( φ ): , Indicates the rotor angle The corresponding pitch; The following formula is used to calculate the profile tooth root radius corresponding to different rotor axial positions: According to the determined parameters, determine the point meshing cycloid segments of the rotor profile corresponding to different rotor axial positions AB , tooth top arc segment BC , pseudo-polynomial curve segment CD , curve segment CD The envelope curve segment DE and tooth root arc segment EA .

7. The design method according to claim 6, characterized in that: By designing the cone angle of the rotor α , rotor center distance A , initial tooth tip radius R 2(0), Cubic spline curve difference points in the rotor pitch law curve A、 point B ,point C with dot D Position and point D The slope k D , the design pseudo polynomial degree of the profile under different corners n ( φ ), the design width angle of the profile line at different turning angles γ ( φ ), adjust the variable pitch variable profile conical screw vacuum pump rotor structure to achieve the adjustment of the working chamber volume change law, optimize and adjust the position distribution, geometric structure and flow conditions of the working chamber leakage channel during gas transportation, and obtain the optimal rotor geometry to meet different needs.

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